# Lesson 13

Usemos gráficas de barras para comparar

## Warm-up: Verdadero o falso: Completemos diez con 9 (10 minutes)

### Narrative

The purpose of this warm-up is to activate students’ previous experiences in which they looked for ways to make a ten—specifically, when one addend is 9. The ability to make a ten will help students develop fluency within 20 and will be helpful later in this lesson and in upcoming lessons when students add and subtract within 20.

When students look for ways to make a ten and notice similarities in the addends and values in each of the expressions, they look for and make use of the structure of whole numbers and the properties of operations (MP7).

### Launch

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

En cada caso, decide si la afirmación es verdadera o falsa. Prepárate para explicar cómo pensaste.

• $$9 + 4 = 9 + 1 + 3$$
• $$9 + 4 = 10 + 3$$
• $$9 + 5 = 10 + 6$$

### Activity Synthesis

• “¿Cómo pueden justificar su respuesta sin sumar?” // "How can you justify your answer without adding?" (I see that 9 + 4 and 9 + 1 + 3 are the same because 1 + 3 = 4.)

## Activity 1: ¿Cuál es la diferencia? (15 minutes)

### Narrative

The purpose of this activity is for students to use a bar graph to compare two quantities and describe the methods they use to find the unknown difference. Monitor for students who draw on the graph and describe ways of finding the difference by counting on or counting back. If students draw on their graph or do not discuss both counting methods during the activity, create and display work so that each method can be discussed during the synthesis. The discrete segments of the bar graph are used to elicit these counting methods (MP5), however, some students may use addition or subtraction, including known sums, to find the difference. Encourage these students to connect their methods to the counting methods shared in the synthesis.

MLR8 Discussion Supports. Provide all students with an opportunity to speak and to practice using comparison statements. Invite students to chorally repeat statements that use “más” // “more” and “menos” // “fewer” in unison 1–2 times.

### Launch

• Groups of 2
• Display the image (graph with no scale).
• “A un grupo de estudiantes de tercer grado le preguntaron: '¿Qué mascotas tienes?'. Sus respuestas se muestran en la gráfica de barras” // “A group of third grade students were asked, ‘What pets do you have?’ Their responses are shown in the bar graph."
• “¿Qué observan sobre los datos en la gráfica? ¿Qué se preguntan?” // "What do you notice about the data in the graph? What do you wonder?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Monitor for students to say: “Más estudiantes tienen gatos que conejos” // “More students have cats than have rabbits,” or wonder, “¿Cuántos estudiantes más tienen gatos que conejos?” // “How many more students have cats than have rabbits?”
• Share and record student responses.
• If students do not make statements using “more” or “fewer,” display:
• “Hay más _____ que _____” // “There are more _____ than _____.”
• “Hay menos _____ que _____” // “There are fewer _____ than _____.”
• “¿Cómo pueden completar las frases para volverlas afirmaciones verdaderas sobre la gráfica?” // “How could you complete the sentences to make them true statements about the graph?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “Ustedes observaron que más estudiantes tienen gatos que conejos. Su trabajo ahora es averiguar cuántos estudiantes más tienen gatos que conejos. Piensen en dos formas diferentes en las que puedan responder y anótenlas” // “You noticed that more students have cats than have rabbits. Your job now is to figure out how many more students have cats than have rabbits. Think about two different ways you can find the answer and record them.”
• 3–4 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for a student who uses a counting on method and a student who uses a counting back method.

### Student Facing

A un grupo de estudiantes de tercer grado les preguntaron: “¿Qué mascotas tienes?”. Sus respuestas se muestran en la gráfica de barras.

¿Qué observas? ¿Qué te preguntas?

Sus respuestas también se muestran en esta gráfica de barras.

¿Cuántos estudiantes más tienen gatos que conejos? Muestra dos formas de encontrar la diferencia.

### Activity Synthesis

• Invite previously identified students to share how they found the difference. If methods are only explained verbally, consider asking, “Muestren cómo pueden contar hacia adelante (o hacia atrás) en la gráfica de barras para hallar cuántos más” // “Can you show us on the bar graph how you could count on (or count back) to find how many more?”
• Record student methods with an equation. For example, for students who describe counting on, write “8 + 9 = 17.”
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // "How are their methods similar? How are their methods different?" (One method starts with the smaller number of pets and counts on to the larger number, like adding 9 more. The other starts with the larger number of pets and counts back to the smaller number, like subtracting 9.)

## Activity 2: Perros en el parque (20 minutes)

### Narrative

The purpose of this activity is for students to use graphs to make comparison statements and solve Compare problems. Students represent their comparisons with equations. In the synthesis, students connect the graph, their comparison statements, and their equations.

When students describe how they see their equations in the graph and how their equations relate to the context, they think abstractly and quantitatively (MP2).

Representation: Access for Perception. Display information in a flexible format to facilitate comparisons. Create a display of the graph with detachable bars, so that types of dogs that do not appear next to each other in the original graph can be more easily compared. For example, number of poodles and number of pugs.
Supports accessibility for: Visual-Spatial Processing, Conceptual Processing

### Launch

• Groups of 2
• Display the Dogs in the Park graph.
• “¿Qué afirmación pueden hacer para comparar el número de huskies con el número de bulldogs?” // “What statement can you make that compares the number of huskies to the number of bulldogs?” (There are more bulldogs than huskies. There are fewer huskies than bulldogs. There are 6 more bulldogs than huskies.)
• 1 minute: partner discussion
• 1 minute: whole-class discussion
• Share statements that use “more” and “fewer.”

### Activity

• “Ahora van a escribir algunas afirmaciones usando las palabras 'más' y 'menos' y a escribir ecuaciones para mostrar cómo encontrar la diferencia” // “Now you are going to write some statements using ‘more’ and ‘fewer’ and write equations to show how to find the difference.”
• 5 minutes: independent work time
• “Ahora revisen con su pareja. ¿Sus afirmaciones son verdaderas?” // “Now check with your partner. Are their statements true?”
• 3 minutes: partner discussion
• Monitor for different equations students use for each comparison.

### Student Facing

Kiran y Lin contaron los tipos de perros que vieron en un parque. Sus datos se muestran en la gráfica de barras.

1. Completa cada espacio para que la afirmación sea verdadera: Hay más

__________________________ que ___________________________.

2. Escribe una ecuación de suma y una de resta para mostrar cuántos más.
3. Completa cada espacio para que la afirmación sea verdadera: Hay menos

___________________________ que ____________________________.

4. Escribe una ecuación de suma y una de resta para mostrar cuántos menos.

### Student Response

If students write statements that are not true, consider asking:

• “¿Cómo decidiste cuál grupo tenía menos?” // "How did you decide which group had fewer?"
• “¿En qué parte de la gráfica ves esto?” // "Where do you see this on the graph?"

### Activity Synthesis

• Invite 1–2 previously identified students to share their statements using fewer and one equation. (Sample response: There are fewer pugs than bulldogs. There are 12 fewer. 8 + 12 = 20)
• Record equation.
• “¿Qué otras ecuaciones podríamos escribir para mostrar ‘cuántos menos‘ en la afirmación de _____?” // “What other equations could we write to show how many fewer for _____’s statement?” (Sample response: We could use subtraction. 20 – 12 = 8 shows you can count back 12 from 20 to get to 8.)
• Record equations.
• For each equation, ask, “¿Qué representa cada número en la ecuación?” // “What does each number represent in the equation?” (20 represents the number of bulldogs. 8 represents the number of pugs. 12 represents how many fewer pugs.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos que hay varias formas en las que podemos hablar sobre comparaciones y escribir ecuaciones para representarlas” // “Today, we learned that there are different ways we can talk about comparisons and write equations to represent them.”

Display graph from Activity 2.

Display: $$14 + 6 = 20$$

“La respuesta es 6. ¿Cuál es la pregunta?” // “6 is the answer. What is the question?” (Sample response: How many more bulldogs are there than huskies?”)

Consider asking: “¿Cómo usaron la gráfica? ¿Qué buscaron?” // “How did you use the graph? What did you look for?”

If time permits (or if $$14 + 6 = 20$$ was discussed in Activity 2 Synthesis):

Display: $$8 - 2 = 6$$

“La respuesta es 2. ¿Cuál es la pregunta?” // “2 is the answer. What is the question?” (Sample response: How many fewer poodles are there than pugs?)

Consider asking: “¿Cómo usaron la gráfica? ¿Qué buscaron?” // “How did you use the graph? What did you look for?”